PEER-REVIEWED ARTICLE bioresources.com Groche & Huttel (2016). “Paperboard forming,” BioResources 11(1), 1855-1867. 1855 Paperboard Forming - Specifics Compared to Sheet Metal Forming Peter Groche* and Dominik Huttel Growing demand for sustainable products has led to increased interest in the use of paperboard as a structural material. Paperboard products are almost exclusively manufactured by embossing, pulp molding, and bending processes. Other well-known forming methods, such as deep or stretch drawing, are only rarely applied to paperboard. This is primarily ascribed to the lack of knowledge concerning the process design and limits when paperboard is employed. In the present work, the applicability of well-established design strategies and characterization methods for metals to paperboard is investigated. Therefore, forming limit diagrams for paperboard are determined in a first step. Additionally, significant material parameters are identified in order to describe the material influence upon the forming limit. Furthermore, the influence of a hydrostatic counter pressure onto the forming limit is investigated. To predict the forming behaviour of a complex formed paperboard demonstration part, a numerical model of a hydroforming process is set up, executed, and validated. Keywords: Hydroforming; Modelling; Paperboard Contact information: Institute for Forming Technology and Machines, Technische Universität Darmstadt, Germany; *Corresponding author: [email protected]INTRODUCTION Life-cycle analyses of paperboard products reveal their attractiveness: the basic fibrous material is renewable, manufactured efficiently in large-scale production processes, light, and recyclable. Furthermore, the properties of paperboard, like its density, strength, surface roughness, and porosity, can be adjusted to meet a wide range of different requirements with the appropriate mechanical treatment, chemical composition, production process parameters, and environmental conditions (Xia 2002; Alava and Niskanen 2006). Paperboard products with developable surfaces, such as plates or folding boxes, are frequently used. More complex, three-dimensional, hollow parts made of paperboard are rare and are produced by pulp moulding, if at all. Other processes, such as deep or stretch drawing, which are well-established for forming metals, are not common in industrial paperboard production. To make use of the advantageous potential of these processes for paperboard, an expansion of production technologies is necessary. Compared to sheet metal, huge deficits exist in terms of constitutive material and friction modelling, characterisation methods, and process technology when deep or stretch drawing should be applied to paperboard. A closer look at metal (DC04 – common deep drawing alloy) and paperboard, as shown in Fig. 1, exhibits the differences in their microscopic structure. Metal consists of a lattice structure. Plastic deformation is enabled by the movement of atomic layers. This is eased by the movement of dislocations, as displayed in Fig. 1a. Paperboard consists of fibres connected by hydrogen
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Paperboard Forming - Specifics Compared to Sheet Metal Forming
Peter Groche* and Dominik Huttel
Growing demand for sustainable products has led to increased interest in the use of paperboard as a structural material. Paperboard products are almost exclusively manufactured by embossing, pulp molding, and bending processes. Other well-known forming methods, such as deep or stretch drawing, are only rarely applied to paperboard. This is primarily ascribed to the lack of knowledge concerning the process design and limits when paperboard is employed. In the present work, the applicability of well-established design strategies and characterization methods for metals to paperboard is investigated. Therefore, forming limit diagrams for paperboard are determined in a first step. Additionally, significant material parameters are identified in order to describe the material influence upon the forming limit. Furthermore, the influence of a hydrostatic counter pressure onto the forming limit is investigated. To predict the forming behaviour of a complex formed paperboard demonstration part, a numerical model of a hydroforming process is set up, executed, and validated.
Keywords: Hydroforming; Modelling; Paperboard
Contact information: Institute for Forming Technology and Machines, Technische Universität Darmstadt,
bonds. These bonds primarily determine the strength of the fibre network (Davidson
1972). Irreversible deformation of paperboard is attributed to the distortion of the web,
the stretching of curled fibres, and the movement of the fibres in the web. The last
deformation mechanism is associated with a release and reshuffling of hydrogen bonds in
the web. A schematic of the irreversible deformation of paperboard is shown in Fig. 1b.
Fig. 1. a) Grinding surface pattern of DC04 and forming mechanisms of metal according to Weißbach (2007); b) surface of paperboard and forming mechanisms
An overview of material testing and modelling methods, as given for sheet metal
(Bruschi et al. 2014), is not available for paperboard. Different authors have focused their
research on modelling strategies for paper and paperboard. They have attempted to find a
reasonable trade-off between model complexity, the effort necessary for parameter
determination, and the reliability of the model predictions. Several researchers have
chosen modelling strategies based on simplified models with a reduced amount of
parameters. Mäkela and Östlund (2003) were able to predict paperboard’s behaviour in
tensile tests using an orthotropic, elastic-plastic material model with associated plasticity.
In the case of corrugated board boxes under load, in addition to the complex
material behaviour, the geometry of the wall structure must be modelled. Jiménez-
Caballero et al. (2009) predicted the deformation characteristics by modelling the
corrugated wall structure and by the use of an orthotropic material model, including
damage and different behaviours in tension and compression. To describe the behaviour
of paperboard in the case of large deformations, as well as for fracturing processes,
enhanced modelling strategies are used. The damaging of paperboard material is
considered to be a sequence of crack initiation, growth, and crack coalescence. Material
laws describing these mechanisms include damage variables and damage evolution laws.
Isaksson et al. (2004) represented experimental tensile test results through the
combination of the damage behaviour and anisotropy of the material by the concept of
Hill (1948). According to Xia (2002), the behaviour of paperboard creasing and folding
processes can be represented as a yield surface build up by sub-surfaces. Hereby, the
anisotropic behaviour, in combination with an associated flow rule, is taken into account.
The paperboard is represented as a multi-layer structure. An interface model, including
damage associated with the inelastic history of the interface displacement, describes the
out-of-plane delamination. The model is capable of describing the experimentally
observed delamination behaviour during creasing and folding processes as well as the
correlations between the bending moment and bending angle (Xia 2002). Further
enhancement of the interface model has allowed for enhanced correlation between
moisture content and varies between 0.65 and 0.72 mm. Tensile tests were performed
with a testing velocity of 10 mm/min. The elongation was measured by a video-
extensometer (built-in video-extensometer of the tensile test machine by the company
Zwick). Furthermore, the behaviour under uniaxial compression was investigated. The
dimensions of the surfaces and thicknesses were determined before and after the
compression tests by an optical measurement system displayed in Fig. 2b and tactile
measurements, respectively. The optical measurement system used two five-megapixel
cameras with a slider distance of 600 mm and 995 mm to the stochastically patterned
surface of the test specimen. A calibration plate of dimensions 145 mm x 170 mm and a
50 mm lens were used (Optical strain measurement system Aramis by GOM – GOM
2011). Figure 2a displays the yield loci for an isotropic material according to von Mises’
assumptions (von Mises 1928) and the anisotropic behaviour according to Hill’s yield
condition for DC04 (1.0338) and paperboard. The direction of the highest tensile flow
stress is defined as the 1-direction, which is the main direction of the fibres in the case of
paperboard. It is obvious that paperboard tends to have significantly higher anisotropy,
associated with the fibre orientation, than common deep drawing metal. Appropriate
constitutive modelling of paperboard must consider this phenomenon.
Figure 2c shows the correlation between the thickness reduction and surface
variation in the compression tests. All materials exhibit larger deviations from volume
constancy for small strains. This could be a result of the levelling of the surface
roughness as well as the influence of elastic deformation. With increasing deformation,
DC04 exhibits the expected volume constancy behaviour. In the case of 6% moisture
content, in equilibrium with the normal climate (23 °C, 50% relative humidity), the
achievable strain is smaller compared to that at 15% moisture content. In relation to the
forming process, the maximum normal pressure during the testing of paperboard is
approximately 6 N/mm². Nevertheless, considering a thickness of 651 ± 8 μm and an
arithmetic mean roughness, Ra, of 6.6 ± 0.5 μm, the measurement point at higher strain
indicates compressible behaviour. Paperboard with 15% moisture content behaves
similarly to DC04 but with a slightly higher gradient, which could be caused by drying
effects and the corresponding coefficient of expansion. During drying, the coefficient of
expansion is three times larger in the thickness direction than the maximum in-plane
coefficient. The experimental findings indicate that volume constancy seems to be a
reasonable assumption in constitutive models, at least for moisture contents above that of
equilibrium within a normal climate.
Fig. 2. a) Yield loci of isotropic, DC04, and paperboard material; b) measurement setup: optical surface measurement system; c) surface εsurface and thickness εthickness strains in compression tests
To predict the producibility of a forming product, the limits of its formability
must be examined. In sheet metal forming, it is common to describe process boundaries
using forming limit diagrams (FLD). To develop these diagrams, different ratios of major
and minor strains are determined by the use of different test setups and geometries. In this
context, the major strain is the maximum surface strain and the minor strain is the
perpendicular strain. The plot of the fracture points in a major-minor strain diagram
enables the definition of forming limits. Strain distributions below the forming limit line
are producible. Strain distributions near or higher than the forming limit line indicate that
the product will fail during the forming process. The forming limits of paperboard are
investigated according to test procedures well-established for the characterisation of
metals (Burschi et al. 2014). More precisely, Table 1 and Fig. 3a display the test setup
and geometry, respectively.
Table 1. Geometrical Data
ga gb gc Gvar (mm)
(mm) (mm) (mm) G0 G1 G2 G3
TS1 12.5 70 - - - - -
TS2 20 3 36 25 50 100 -
TS4 30 20 60 plate 20 80 -
TS5 60/60/50 20 60 plate 10 15 22.5/10
Fig. 3. a) Test setup and geometries; b) surface strain at fracture; c) definition of fracture time by strain rate diagram; d) calculation of ε1 strain by a parabola fit according to ISO 12004; e) strain calculation in case of ε2 strain
Ordinary tensile tests, tensile tests with notched samples, and Nakazima
(Nakazima et al. 1971) tests were carried out. Additionally, bulge tests with a carrying
layer and perforated samples, as proposed by Banabic et al. (2013), were performed. An
optical surface measurement system (Aramis by GOM, Germany) was used for online
strain measurement. Figure 3b displays the surface strain at the point of fracture. This
the sample was cut out (time less than 2 seconds) and the weight was measured. After
this, the material was dried at 105°C to get the dry weight. This made it possible to
calculate the moisture content right after the friction test procedure with heated tools. It
can be seen that a testing temperature of approximately 140 °C led to a drying of the
material to 0% moisture. This exemplifies the need for separation of the sample and
friction measurement tool before the start of the testing process. The change in moisture
content before testing can significantly change the determined friction.
Fig. 6. a) Friction for DC04 (Filzek 2006) (tool material: 0.7060; lubricant: oil; and paperboard (tool material: 1.2085; lubricant: none; b) tool temperature – material – moisture – interaction
TECHNOLOGY
The previously described forming properties of paperboard show the need for
control of temperature, moisture, and hydrostatic pressure during forming processes.
Forming tools designed to meet these requirements are displayed in Fig. 7. Process 1 is a
gas hydroforming process in which a film is used to separate the paperboard from the
pressurised air. The blank-holder is controlled and can be heated. Process 2 makes use of
a liquid for the forming process. A counter pressure can be applied. It has two functions:
support of the material during the forming process and inhibition of wrinkling of the
paperboard. This flexible blank-holder enables the material to flow from the outer area
such that wrinkles can be suppressed. Abaqus (v. 6.12) was used to simulate the forming
process. The dimensions of the forming tool and assembly are presented in Fig. 7c. The
material behaviour is represented by Hill’s flow function, as shown in Fig. 2. The mesh
consists of two elements in the thickness direction with an edge ratio of three. A dynamic
implicit (Hilber-Hughes-Taylor-Integration) solver is used.
Fig. 7. Forming tool, geometry and FEA setup (Huttel and Groche 2014), a) process 1, b) process 2 with hydrostatic pressure support, c) geometry and FEA
Material data and the paperboard-tool interaction properties described in the
previous sections form the basis for the numerical simulations of the forming processes.
Figure 8a displays the comparison between the FEA (Finite Element Analysis) and
experimental investigations based on the surface strain determination according to Eq. 1,
εvo=(ε112+ε22
2)0.5 (1)
The strain distributions on the surfaces are transferred into the OBFLD. In the
case of Forming Process 1, with 15% moisture content at RT, the FEA investigations in
Fig. 8b predict that the material will fail during the forming process. This was confirmed
by the experimental results shown in Fig. 8a. A change of the tool temperature affects,
among other things, the coefficient of friction and thus, the surface strain distribution, as
presented in Fig. 8b. In the case of the 140 °C and 200 N blank-holder force, a product
without fracture was predicted. An increase of the blank-holder-force to 1000 N led to
crossing of the forming limit (fo) but not the fracture limit (fr) in the OBFLD (see Fig. 8c).
This implies that the process conditions were in a range in which failure could occur for
some material batches. Figure 8d displays the surface failure occurring in the
experimental investigation. The numerical material description considers a change of
friction and a change of the initial material properties in the blank holder area as a result
of drying processes. Furthermore, the drying of the whole material after the forming
process is simulated by moisture-strain relations.
Fig. 8. Experimental and numerical investigation of the forming limit: a) Process 1: 200 N blank-holder force (bhf), b) numerical simulation of the failure behaviour, c) OBFLD in case of 1000 N bhf, d) surface fracture, e) Process 2, f) OBFLD of Process 2
The influence of counter pressure on the forming limits was studied by means of
Process 2. Identical material settings, temperatures, and tools as those in Process 1 were
used. As can be seen from Fig. 8e, the formability of the material was considerably
enhanced. Experimental and FEA results yielded fracture-free surfaces of the formed
paperboard samples. The enhancement of the forming limits is represented in Fig. 8f. All
surface strain combinations remained underneath the forming limit line for a hydrostatic
Comparisons of the geometric and mechanical quantities are displayed in Fig. 9.
The comparison between the final geometries resulting from the experimental and
numerical investigations for Process 1 at RT is presented in Fig. 9a. FEA predicts the
final shape of the product with high accuracy. Differences can be seen at the edge of the
geometry. These can be affected by the drying process. Plane stress components in
material direction 1 for cross sections of 0° and 90° are displayed in Fig. 9b. In this
respect, Processes 1 and 2 exhibited similarities. The reason for the different failure
behaviours in Processes 1 and 2 is visible in Fig. 9c. The stress components in the z or
thickness directions differ because of the counter pressure superimposed in Process 2.
Fig. 9. Experimental and numerical investigation of the forming process (Huttel and Groche 2014): a) comparison of the geometry; b) stress in 1 direction; c) stress in z direction
DISCUSSION
Differences between metal and paperboard are most distinct with respect to their
anisotropy and the sensitivity of the material and friction properties on changes in
moisture content and temperature. Nevertheless, adapted characterisation, simulation, and
design methods are widely transferrable from metal to paperboard. Additionally, the
drying of paperboard after forming must be carefully considered to predict the final
paperboard geometry accurately. Process design can be carried out with the material data
gained. Superposed counter pressure is a suitable measure to effectively reduce failure
probability.
Based on these findings, forming processes for paperboard can be systematically
developed. Figure 10 displays an example of a process design aiming for producible
product geometry. Starting with an initial design, wrinkles and fracture are detected (e.g.,
Fig. 8a).
In the next step, wrinkles are minimised by geometry adaption and modified
material orientation (Fig. 10b). The OBFLD displays fracture areas. This enables the
adaptation of geometry to achieve a sound product (Fig. 10c). The final process design
step is experimental verification.
Figure 10d shows the result: a product without wrinkles or fracture. This shows
that an FEA-based design strategy for paperboard has the capability to develop
systematically producible products made of paperboard.
Fig. 10. Design strategy for the development of paperboard products: a) starting geometry, b) suppressed wrinkles, c) optimised result, d) final product
CONCLUSIONS
1. Formed products made of paperboard are highly attractive from mechanical and
environmental viewpoints.
2. However, because of their fibrous structure, well-established modelling, testing, and
design approaches used in metal forming can hardly be used.
3. Paperboard’s behaviour and tribological conditions are strongly dependent on its
moisture content and temperature. Both influencing parameters must be considered in
process modelling and process design.
4. The formability of paperboard can be increased drastically by superimposed
hydrostatic pressure.
5. Well-adjusted process conditions enable high plastic deformation.
6. These conditions can be used to form environmentally sound products by deep and
stretch drawing. New products, as well as new areas of application for paperboard,
are within reach.
ACKNOWLEDGMENTS
The presented investigations were carried out within the research projects
GR1818/37-1 and IGF–17788N. The authors wish to thank the German Research
Foundation (DFG), the Federal Ministry for Economic Affairs and Energy (BMWI), and
the German Federation of Industrial Research Associations (AiF) for supporting the